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%I #76 Oct 26 2020 23:01:11
%S 18,20,21,54,147,342,602,889,258121
%N Numbers k such that A019320(k) is greater than A064078(k) and the latter is a prime or a prime power.
%C The unique prime factor of A064078(k) is then a unique prime to base 2 (see A161509), but not a cyclotomic number.
%C Subsequence of A161508. In fact, subsequence of the set difference A161508 \ A072226.
%C In all known examples, A064078(k) is a prime. If A064078(k) was a prime power p^j with j>1, then p would be both a Wieferich prime (A001220) and a unique prime to base 2.
%C Subsequence of A093106 (the characterization of A093106 can be useful when searching for more terms).
%C Should this sequence be infinite?
%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=Phi%28258121%2C2%29%2F719">Phi(258121,2)/719</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Unique_prime#Binary_unique_primes">Unique prime, section Binary unique primes</a>.
%o (PARI) for(n=1,+oo,c=polcyclo(n,2); c % n < 2 && next(); c/=(c%n); ispseudoprime(if(ispower(c,,&b),b,c))&&print1(n, ", "))
%Y Cf. A019320, A064078, A093106, A072226, A144755, A161508, A161509, A247071.
%K nonn,hard,more
%O 1,1
%A _Jeppe Stig Nielsen_, Sep 22 2020